Many textbooks teach a rule of thumb stating that the mean is right of the median under right skew, and left of the median under left skew but this is not always true.
According to wikipedia, there is no simple closed form for the median of the Gamma distribution.
Intuitively, I would think that the mean is always left to the median in the Gamma distribution. The mean would eventually be roughly equal to the median when the shape parameter $\alpha$ is very big. Is my intuition correct?